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General Topology [Dixmier, J]

Topic: General Topology

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General Topology [John L. Kelley]

Topic: General Topology

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Jun 29, 2018
06/18

by
Jean Goubault-Larrecq; Kok Min Ng

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Using the notion of formal ball, we present a few easy, new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its $d$-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower semicontinuous $\bar{\mathbb{R}}_+$-valued function is the supremum of a chain of Lipschitz...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1606.05445

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Jun 28, 2018
06/18

by
Olena Karlova

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We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb R$ which is not Baire measurable. We show that if $X$ is a product of normed spaces $X_n$, $a\in X$ and $\sigma(a)=\{x\in X:|\{n\in\mathbb N: x_n\ne a_n\}|

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1508.01366

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Jun 28, 2018
06/18

by
Richard Lupton; Max F. Pitz

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This paper investigates the space $C_k(\omega^*,\omega^*)$, the space of continuous self-maps on the Stone-\v{C}ech remainder of the integers, $\omega^*$, equipped with the compact-open topology. Our main results are that (1) $C_k(\omega^*,\omega^*)$ is Baire, (2) Stone-\v{C}ech extensions of injective maps on $\omega$ form a dense set of weak $P$-points in $C_k(\omega^*,\omega^*)$, (3) it is independent of ZFC whether $C_k(\omega^*,\omega^*)$ contains $P$-points, and that (4)...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1509.04985

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Jun 30, 2018
06/18

by
Sergey Medvedev

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We show that if a separable space X has a meager open subset containing a copy of the Cantor set 2^\omega, then X has $\frak{c}$ types of countable dense subsets. We suggest a generalization of the \lambda-set for non-separable spaces. Let X be an h-homogeneous \Lambda-set. Then X is densely homogeneous and (X \setminus A) is homeomorphic to X for every \sigma-discrete A \subset X.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1401.7964

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Jun 30, 2018
06/18

by
Jesús P. Moreno-Damas

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We define the bounded coarse structure attached to a family of pseudometrics and give some counterexamples to conjectures that arise naturally.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1410.2763

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Jun 30, 2018
06/18

by
Alan Dow; Klaas Pieter Hart

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We prove that the Cech-Stone remainder of the real line has a family of 2^c mutually non-homeomorphic subcontinua. We also exhibit a consistent example of a first-countable continuum that is not a continuous image of this remainder.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1401.3132

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Jun 26, 2018
06/18

by
Michael Megrelishvili; Luie Polev

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A Hausdorff topological group is called minimal if it does not admit a strictly coarser Hausdorff group topology. This paper mostly deals with the topological group $H_+(X)$ of order-preserving homeomorphisms of a compact linearly ordered connected space $X$. We provide a sufficient condition on $X$ under which the topological group $H_+(X)$ is minimal. This condition is satisfied, for example, by: the unit interval, the ordered square, the extended long line and the circle (endowed with its...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1501.03410

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Jun 28, 2018
06/18

by
Alan Dow; Rodrigo Hernández-Gutiérrez

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We give a partial solution to a question by Alas, Junqueria and Wilson by proving that under PFA the one-point compactification of a locally compact, discretely generated and countably tight space is also discretely generated. After this, we study the cardinal number given by the smallest possible character of remote and far sets of separable metrizable spaces. Finally, we prove that in some cases a countable space has far points.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1509.01601

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Jun 28, 2018
06/18

by
Paul Gartside; Max F. Pitz; Rolf Suabedissen

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The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\mathcal{D}(X)=\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more...

Topics: Combinatorics, Mathematics, General Topology

Source: http://arxiv.org/abs/1509.07769

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Jun 27, 2018
06/18

by
Taras Banakh; Alex Ravsky

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For any topological space $X$ we study the relation between the universal uniformity $\mathcal U_X$, the universal quasi-uniformity $q\mathcal U_X$ and the universal pre-uniformity $p\mathcal U_X$ on $X$. For a pre-uniformity $\mathcal U$ on a set $X$ and a word $v$ in the two-letter alphabet $\{+,-\}$ we define the verbal power $\mathcal U^v$ of $\mathcal U$ and study its boundedness numbers $\ell(\mathcal U^v)$ and $\bar \ell(\mathcal U^v)$. The boundedness numbers of the (Boolean operations...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.04480

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Jun 27, 2018
06/18

by
J. F. Peters; C. Guadagni

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This article introduces strongly proximal continuous (s.p.c.) functions, strong proximal equivalence (s.p.e.) and strong connectedness. A main result is that if topological spaces $X,Y$ are endowed with compatible strong proximities and $f:X\longrightarrow Y$ is a bijective s.p.e., then its extension on the hyperspaces $\CL(X)$ and $\CL(Y)$, endowed with the related strongly hit and miss hypertopologies, is a homeomorphism. For a topological space endowed with a strongly near proximity,...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1504.02740

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Jun 27, 2018
06/18

by
Ashwini K. Amarasinghe

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We shall prove that the Hilbert cube cannot be separated by a weakly infinite dimensional subset. As a corollary we obtain that the complement of a weakly infinite dimensional subset of the space of complete non negatively curved metrics is continuum connected. We can extend this result to the associated moduli space when the set removed is a Hausdorff space with Haver's property C. These results are refinements of theorems proven by Belegradek and Hu.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1505.04452

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Jun 28, 2018
06/18

by
S. S. Gabriyelyan; S. A. Morris

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It is proved that any surjective morphism $f: \mathbb{Z}^\kappa \to K$ onto a locally compact group $K$ is open for every cardinal $\kappa$. This answers a question posed by Karl Heinrich Hofmann and the second author.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1508.00775

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Jun 30, 2018
06/18

by
Fu-Gui Shi; Zhen-Yu Xiu

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In this paper, the notion of $(L,M)$-fuzzy convex structures is introduced. It is a generalization of $L$-convex structures and $M$-fuzzifying convex structures. In our definition of $(L,M)$-fuzzy convex structures, each $L$-fuzzy subset can be regarded as an $L$-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of $(L,M)$-fuzzy convex structures, the concepts of quotient structures, substructures...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1702.03521

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Jun 28, 2018
06/18

by
John Reynolds

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We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space are pretopological notions. Additionally, we define a version of H-closedness for pretopological spaces and investigate the properties of such a space.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1510.08044

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Jun 28, 2018
06/18

by
K. Abodayeh; N. Mlaiki; T. Abdeljawad; W. Shatanawi

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Very recently, Mehadi et al [M. Asadi, E. Karap{\i}nar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on $M-$metric spaces] extended the partial metric spaces to the notion of $M-$metric spaces. In this article, we study some relations between partial metric spaces and $M-$metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to $M-$metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karap\i nar...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.06611

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Jun 29, 2018
06/18

by
E. Makai,; E. Peyghan; B. Samadi

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We investigate weak and strong structures for generalized topological spaces, among others products, sums, subspaces, quotients, and the complete lattice of generalized topologies on a given set. Also we introduce $T_{3.5}$ generalized topological spaces and give a necessary and sufficient condition for a generalized topological space to be a $T_{3.5}$ space: they are exactly the subspaces of powers of a certain natural generalized topology on $[0,1]$. For spaces with at least two points here...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1604.02881

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Jun 29, 2018
06/18

by
V. Mykhaylyuk

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We give a characterization of countable discrete subspace $A$ of a topological space $X$ such that there exists a (linear) continuous mapping $\varphi:C_p^*(A)\to C_p(X)$ with $\varphi(y)|_A=y$ for every $y\in C_p^*(A)$. Using this characterization we answer two questions of A.~Arhangel'skii. Moreover, we introduce the notion of well-covered subset of a topological space and prove that for well-covered functionally closed subset $A$ of a topological space $X$ there exists a linear continuous...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1604.06178

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Jun 29, 2018
06/18

by
Anubha Jindal; R. A. McCoy; S. Kundu; Varun Jindal

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This paper studies various completeness properties of the open-point and bi-point-open topologies on the space C(X) of all real-valued continuous functions on a Tychonoff space X. The properties range from complete metrizability to the Baire space property.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1607.01491

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Jun 30, 2018
06/18

by
István Juhász; Lajos Soukup; Zoltán Szentmiklóssy

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Given cardinals ${\lambda}$ and ${\mu}$ we say that $[\mathbf B({\lambda})]^C$ is ${\mu}$-colorable if there is a coloring $f:\mathbf B({\lambda})\to{\mu}$ such that $f"Z={\mu}$ whenever a subspace $Z\subset \mathbf B({\lambda})$ is homeomorphic to the Cantor set, where $\mathbf B({\lambda})$ denotes the Baire space of weight ${\lambda}$. We prove that a crowded feebly compact regular space $X$ is ${\mu}$-resolvable provided $[\mathbf B({\lambda})]^C$ is ${\mu}$-colorable for each...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1702.02454

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Jun 30, 2018
06/18

by
Igor Protasov; Ksenia Protasova

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A ballean (or coarse structure) is a set endowed with some family of subsets, the balls, is such a way that balleans with corresponding morphisms can be considered as asymptotic counterparts of uniform topological spaces. For a ballean $\mathcal{B}$ on a set $X$, the hyperballean $\mathcal{B}^{\flat}$ is a ballean naturally defined on the set $X^{\flat}$ of all bounded subsets of $X$. We describe all balleans with hyperballeans of bounded geometry and analyze the structure of these...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1702.07941

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Jun 30, 2018
06/18

by
Jacopo Somaglia

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The aim of this note is to characterize trees, endowed with coarse wedge topology, that have a retractional skeleton. We use this characterization to provide new examples of non-commutative Valdivia compact spaces that are not Valdivia.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1703.05655

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Jun 29, 2018
06/18

by
Antonio Avilés; Grzegorz Plebanek

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We introduce the notion that a zero-dimensional compact space $L$ is a \emph{Boolean image} of an arbitrary compact space $K$. When $K$ is also zero-dimensional, this just means that $L$ is a continuous image of $K$. However, a number of interesting questions arise when we consider connected compacta $K$.

Topics: General Topology, Logic, Mathematics

Source: http://arxiv.org/abs/1610.04829

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Jun 30, 2018
06/18

by
Leandro F. Aurichi; Lyubomyr Zdomskyy

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We present an internal characterization for the productively Lindel\"of property, thus answering a long-standing problem attributed to Tamano. We also present some results about the relation Alster spaces vs. productively Lindel\"of spaces.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1704.03843

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Jun 30, 2018
06/18

by
Amar Kumar Banerjee; Apurba Banerjee

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In this paper we have studied the idea of ideal completeness of function spaces Y to the power X with respect to pointwise uniformity and uniformity of uniform convergence. Further involving topological structure on X we have obtained relationships between the uniformity of uniform convergence on compacta on Y to the power X and uniformity of uniform convergence on Y to the power X in terms of I-Cauchy condition and I-convergence of a net. Also using the notion of a k-space we have given a...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1704.05279

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Jun 30, 2018
06/18

by
N. Albuquerque; L. Bernal-Gonzalez; D. Pellegrino; J. B. Seoane-Sepulveda

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The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from the real line $\mathbb{R}$ to any Euclidean space $\mathbb{R}^n$. The algebraic structure of the set of these functions (as well as extensions to spaces with higher dimensions) is analyzed from the modern point of view of lineability, and large algebras are found within the...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1404.5876

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Jun 30, 2018
06/18

by
Ol'ga Sipacheva

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It is proved that the existence of a countable extremally disconnected Boolean topological group containing a family of open subgroups whose intersection has empty interior implies the existence of a rapid ultrafilter.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1405.6356

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Jun 30, 2018
06/18

by
Boaz Tsaban

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Which Isbell--Mr\'owka spaces ($\Psi$-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a $\Psi$-space that is (strongly) star-Menger but not star-Hurewicz is obtained. The PCF-theory function $\kappa\mapsto\cof([\kappa]^\alephes)$ is a key tool. Using the method of forcing, a complete answer to a question of Bonanzinga and Matveev is provided. The...

Topics: Mathematics, General Topology, Logic

Source: http://arxiv.org/abs/1405.7208

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Jun 30, 2018
06/18

by
Cetin Vural

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We obtained some upper bounds for the pseudocharacter of the space C(X,Y) at a point f.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1406.6839

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Jun 30, 2018
06/18

by
István Juhász; Lajos Soukup; Zoltán Szentmiklóssy

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Given a property $P$ of subspaces of a $T_1$ space $X$, we say that $X$ is {\em $P$-bounded} iff every subspace of $X$ with property $P$ has compact closure in $X$. Here we study $P$-bounded spaces for the properties $P \in \{\omega D, \omega N, C_2 \}$ where $\omega D \, \equiv$ "countable discrete", $\omega N \, \equiv$ "countable nowhere dense", and $C_2 \,\equiv$ "second countable". Clearly, for each of these $P$-bounded is between countably compact and...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1406.7805

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Jun 30, 2018
06/18

by
M. J. Chasco

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It is proved that, for a wide class of topological abelian groups (locally quasi--convex groups for which the canonical evaluation from the group into its Pontryagin bidual group is onto) the arc component of the group is exactly the union of the one--parameter subgroups. We also prove that for metrizable separable locally arc-connected reflexive groups, the exponential map from the Lie algebra into the group is open.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1407.1178

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Jun 30, 2018
06/18

by
Hichem Ben-El-Mechaiekh

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The purpose of this note is to generalize the celebrated Ran and Reurings fixed point theorem to the setting of a space with a binary relation that is only transitive (and not necessarily a partial order) and a relation-complete metric. The arguments presented here are simple and straightforward. It is also shown that extensions by Rakotch and Hu-Kirk of Edelstein's generalization of the Banach contraction principle to local contractions on chainable complete metric spaces derive from the...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1411.4698

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Jun 26, 2018
06/18

by
J. M. Almira; A. J. López-Moreno; N. Del Toro

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In this note, we give several definitions of metric corona properties which could be of interest in Set Topology, Functional Analysis and Approximation Theory, and prove that there are complete metrizable t.v.s. which are nice in the sense that they have a metric which is invariant by translations, but they do not have good corona properties. All classical function spaces satisfy good corona properties but it is an open question to know if this also holds for the more general setting of locally...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1502.03383

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Jun 30, 2018
06/18

by
Olena Karlova; Volodymyr Mykhaylyuk

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We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a strongly separately continuous mapping to be continuous on a product of an arbitrary family of topological spaces. Moreover, we charac\-terize the discontinuity point set of strongly separately continuous function defined on a subset of countable product of...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1411.6886

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Jun 30, 2018
06/18

by
Robert Leek

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In this paper, we will use investigate the existence of compactifications with particular convergence properties - pseudoradial, radial, sequential and Fr\'echet-Urysohn - through the use of spoke systems.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1412.8701

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Jun 27, 2018
06/18

by
Taras Radul

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This paper studies n-player games where players beliefs about their opponents behaviour are capacities. The concept of an equilibrium under uncertainty was introduced J.Dow and S.Werlang (J Econ. Theory 64 (1994) 205--224) for two players and was extended to n-player games by J.Eichberger and D.Kelsey (Games Econ. Behav. 30 (2000) 183--215). Expected utility was expressed by Choquet integral. We consider the concept of an equilibrium under uncertainty in this paper but with expected utility...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.00563

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Jun 27, 2018
06/18

by
Paolo Lipparini

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The class $\mathfrak C $ relative to countably compact topological spaces and the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z. Frol\'ik are naturally generalized relative to every topological property. We provide a characterization of such generalized Frol\'ik classes in the broad case of properties defined in terms of filter convergence. If a class of spaces can be defined in terms of filter convergence, then the same is true for its Frol\'ik class.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.02277

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Jun 27, 2018
06/18

by
J. F. Peters; C. Guadagni

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This article introduces the {\it strongly hit and far-miss as well as hit and strongly far miss hypertopologies on $\textrm{CL}(X)$ associated with} ${\mathscr{B}}$, a nonempty family of subsets on the topological space $X$. They result from the strong farness and strong nearness proximities. The main results in this paper stem from the Hausdorffness of $(\textrm{CL}(X), \tau_{\doublevee, \mathscr{B}})$ and $(\textrm{RCL}(X), \tau^\doublewedge_\mathscr{B} ) $, where $\textrm{RCL}(X)$ is the...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1503.02587

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Jun 27, 2018
06/18

by
Szymon Plewik; Marta Walczyńska

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Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric $\sigma$-discrete spaces. Some related topics are also explored. For example: For each infinite cardinal number $\frak m$, there exist $2^{\frak m}$ many non-homeomorphic metric scattered spaces of the cardinality $\frak m $; If $X \subseteq \omega_1$ is a...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1504.08130

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Jun 27, 2018
06/18

by
Raushan Z. Buzyakova

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We identify a condition on X that guarantees that any finite power of X is homeomorphic to a subspace of a linearly ordered space

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1505.02319

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Jun 30, 2018
06/18

by
Andrea Medini

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All spaces are assumed to be separable and metrizable. Our main result is that the statement "For every space $X$, every closed subset of $X$ has the perfect set property if and only if every analytic subset of $X$ has the perfect set property" is equivalent to $\mathfrak{b}>\omega_1$ (hence, in particular, it is independent of $\mathsf{ZFC}$). This, together with a theorem of Solecki and an example of Miller, will allow us to determine the status of the statement "For every...

Topics: Mathematics, General Topology, Logic

Source: http://arxiv.org/abs/1405.0191

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Jun 30, 2018
06/18

by
Alan Dow; Todd Eisworth

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We show that the Continuum Hypothesis is consistent with all regular spaces of hereditarily countable $\pi$-character being C-closed. This gives us a model of ZFC in which the Continuum Hypothesis holds and compact Hausdorff spaces of countable tightness are sequential.

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1409.0579

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Jun 30, 2018
06/18

by
Boris Šobot

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After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \beta N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on \beta N and we introduce a few more, defined in a natural way. For some of them we find equivalent conditions for divisibility. Finally, we mention a few facts about prime and irreducible elements of (\beta N, \cdot). The motivation behind all this...

Topics: Mathematics, General Topology

Source: http://arxiv.org/abs/1410.6778

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Jun 30, 2018
06/18

by
Dominique Lecomte; Miroslav Zeleny

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We construct, for each countable ordinal $\xi$, a closed graph with Borel chromatic number two and Baire class $\xi$ chromatic number $\aleph\_0$.

Topics: Mathematics, General Topology, Logic

Source: http://arxiv.org/abs/1406.7544

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Jun 28, 2018
06/18

by
Marita Ferrer; Salvador Hernandez; Luis Tarrega

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Combining ideas of Troallic and Cascales, Namioka, and Vera, we prove several characterizations of \textit{almost equicontinuity} and \textit{hereditary almost equicontinuity} for subsets of metric-valued continuous functions when they are defined on a \v{C}ech-complete space. We also obtain some applications of these results to topological groups and dynamical systems.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1511.05021

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Jun 28, 2018
06/18

by
K. Abodayeh; A. Pitea; W. Shatanawi; T. Abdeljawad

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In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1512.03771

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Jun 29, 2018
06/18

by
Borys Álvarez-Samaniego; Andrés Merino

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We consider the class of compact countable subsets of the real numbers $\mathbb{R}$. By using an appropriate partition, up to homeomorphism, of this class we give a detailed proof of a result shown by S. Mazurkiewicz and W. Sierpinski related to the cardinality of this partition. Furthermore, for any compact subset of $\mathbb{R}$, we show the existence of a "primitive" related to its Cantor-Bendixson derivative.

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1605.00853

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Jun 28, 2018
06/18

by
Friedrich Martin Schneider

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Garret Birkhoff's HSP theorem characterizes the classes of models of algebraic theories as those being closed with respect to homomorphic images, subalgebras, and products. In particular, it implies that an algebra $\mathbf{B}$ satisfies all equations that hold in an algebra $\mathbf{A}$ of the same type if and only if $\mathbf{B}$ is a homomorphic image of a subalgebra of a (possibly infinite) direct power of $\mathbf{A}$. The former statement is equivalent to the existence of a natural map...

Topics: Logic, Mathematics, General Topology

Source: http://arxiv.org/abs/1510.03166